Optimal control in infinite horizon problems: A Sobolev space approach

In this paper, we make use of the Sobolev space W exp.1,1 (R+, R exp.n) to derive at once the Pontryagin conditions for the standard optimal growth model in continuous time, including a necessary and sufficient transversality condition. An application to the Ramsey model is given. We use an order ideal argument to solve the problem inherent to the fact that L exp.1 spaces have natural positive cones with no interior points.